Path-based system optimal dynamic traffic assignment models: Formulations and solution methods

The evaluation of path marginal cost, i.e., the gradient of the objective function with respect to path flows, lies in the kernel of solution algorithms for path-based SODTA models. We identify a common critical deficiency in existing path marginal cost evaluation methods, develop a new path marginal cost evaluation method by tracing path flow perturbation propagations and design the corresponding solution algorithm for path-based SO-DTA models in networks in mono-centric cities. Our numerical experiments indicate that this algorithm can generate numerical solutions close to analytical solutions while the solution scheme based on the existing path marginal cost evaluation method cannot.